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Unified treatment and classification of superintegrable systems with integrals quadratic in momenta on a two-dimensional manifold

J. Math. Phys. 47, 042904 (2006); doi:10.1063/1.2192967

Published 28 April 2006

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C. Daskaloyannis
Mathematics Department, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece

K. Ypsilantis
Physics Department, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
In this paper we prove that the two-dimensional superintegrable systems with quadratic integrals of motion on a manifold can be classified by using the Poisson algebra of the integrals of motion. There are six general fundamental classes of superintegrable systems. Analytic formulas for the involved integrals are calculated in all the cases. All the known superintegrable systems are classified as special cases of these six general classes. ©2006 American Institute of Physics
History: Received 31 January 2005; accepted 15 March 2006; published 28 April 2006
Permalink: http://link.aip.org/link/?JMAPAQ/47/042904/1
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KEYWORDS and PACS

Keywords
PACS
  • 02.30.Rz
    Integral equations
  • 02.30.Jr
    Partial differential equations
  • 02.60.Lj
    Ordinary and partial differential equations; boundary value problems
  • 02.60.Nm
    Integral and integrodifferential equations
  • 02.10.Ud
    Linear algebra
  • YEAR: 2006

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ISSN:
0022-2488 (print)   1089-7658 (online)
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